Muutke küpsiste eelistusi

Computability and Logic 5th Revised edition [Pehme köide]

4.12/5 (298 hinnangut Goodreads-ist)
(Princeton University, New Jersey), ,
  • Formaat: Paperback / softback, 366 pages, kõrgus x laius x paksus: 254x178x19 mm, kaal: 650 g, Worked examples or Exercises
  • Ilmumisaeg: 17-Sep-2007
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521701465
  • ISBN-13: 9780521701464
Teised raamatud teemal:
Computability and Logic 5th Revised editionSuurem pilt
  • Formaat: Paperback / softback, 366 pages, kõrgus x laius x paksus: 254x178x19 mm, kaal: 650 g, Worked examples or Exercises
  • Ilmumisaeg: 17-Sep-2007
  • Kirjastus: Cambridge University Press
  • ISBN-10: 0521701465
  • ISBN-13: 9780521701464
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780521701464.html
Märksõnad:
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. This 2007 fifth edition has been thoroughly revised by John Burgess. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems. This updated edition is also accompanied by a website as well as an instructor's manual.

Arvustused

' gives an excellent coverage of the fundamental theoretical results about logic involving computability, undecidability, axiomatization, definability, incompleteness, etc.' American Math Monthly 'The writing style is excellent: Although many explanations are formal, they are perfectly clear. Modern, elegant proofs help the reader understand the classic theorems and keep the book to a reasonable length.' Computing Reviews ' a valuable asset to those who want to enhance their knowledge and strengthen their ideas in the areas of artificial intelligence, philosophy, theory of computing, discrete structures, mathematical logic. It is also useful to teachers for improving their teaching style in these subjects.' Computer Engineering

Muu info

Computability and Logic is a classic because of its accessibility to students without a mathematical background. This fifth edition was first published in 2007.
Preface to the Fifth Edition xi
COMPUTABILITY THEORY
Enumerability
3(13)
Enumerability
3(4)
Enumerable Sets
7(9)
Diagonalization
16(7)
Turing Computability
23(12)
Uncomputability
35(10)
The Halting Problem
35(5)
The Productivity Function
40(5)
Abacus Computability
45(18)
Abacus Machines
45(6)
Simulating Abacus Machines by Turing Machines
51(6)
The Scope of Abacus Computability
57(6)
Recursive Functions
63(10)
Primitive Recursive Functions
63(7)
Minimization
70(3)
Recursive Sets and Relations
73(15)
Recursive Relations
73(7)
Semirecursive Relations
80(3)
Further Examples
83(5)
Equivalent Definitions of Computability
88(13)
Coding Turing Computations
88(6)
Universal Turing Machines
94(2)
Recursively Enumerable Sets
96(5)
BASIC METALOGIC
A Precis of First-Order Logic: Syntax
101(13)
First-Order Logic
101(5)
Syntax
106(8)
A Precis of First-Order Logic: Semantics
114(12)
Semantics
114(5)
Metalogical Notions
119(7)
The Undecidability of First-Order Logic
126(11)
Logic and Turing Machines
126(6)
Logic and Primitive Recursive Functions
132(5)
Models
137(16)
The Size and Number of Models
137(5)
Equivalence Relations
142(4)
The Lowenheim-Skolem and Compactness Theorems
146(7)
The Existence of Models
153(13)
Outline of the Proof
153(3)
The First Stage of the Proof
156(1)
The Second Stage of the Proof
157(3)
The Third Stage of the Proof
160(2)
Nonenumerable Languages
162(4)
Proofs and Completeness
166(21)
Sequent Calculus
166(8)
Soundness and Completeness
174(5)
Other Proof Procedures and Hilbert's Thesis
179(8)
Arithmetization
187(12)
Arithmetization of Syntax
187(5)
Godel Numbers
192(4)
More Godel Numbers
196(3)
Representability of Recursive Functions
199(21)
Arithmetical Definability
199(8)
Minimal Arithmetic and Representability
207(5)
Mathematical Induction
212(4)
Robinson Arithmetic
216(4)
Indefinability, Undecidability, Incompleteness
220(12)
The Diagonal Lemma and the Limitative Theorems
220(4)
Undecidable Sentences
224(2)
Undecidable Sentences without the Diagonal Lemma
226(6)
The Unprovability of Consistency
232(11)
FURTHER TOPICS
Normal Forms
243(17)
Disjunctive and Prenex Normal Forms
243(4)
Skolem Normal Form
247(6)
Herbrand's Theorem
253(2)
Eliminating Function Symbols and Identity
255(5)
The Craig Interpolation Theorem
260(10)
Craig's Theorem and Its Proof
260(4)
Robinson's Joint Consistency Theorem
264(1)
Beth's Definability Theorem
265(5)
Monadic and Dyadic Logic
270(9)
Solvable and Unsolvable Decision Problems
270(3)
Monadic Logic
273(2)
Dyadic Logic
275(4)
Second-Order Logic
279(7)
Arithmetical Definability
286(9)
Arithmetical Definability and Truth
286(3)
Arithmetical Definability and Forcing
289(6)
Decidability of Arithmetic without Multiplication
295(7)
Nonstandard Models
302(17)
Order in Nonstandard Models
302(4)
Operations in Nonstandard Models
306(6)
Nonstandard Models of Analysis
312(7)
Ramsey's Theorem
319(8)
Ramsey's Theorem: Finitary and Infinitary
319(3)
Konig's Lemma
322(5)
Modal Logic and Provability
327(14)
Modal Logic
327(7)
The Logic of Provability
334(3)
The Fixed Point and Normal Form Theorems
337(4)
Annotated Bibliography 341(2)
Index 343